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Look at the dice stacked below. Though you can't see it, the faces that touch other dice all share the same number. If that's the case, which number should go on the the question mark?
All of these dice have the same layout of numbers.
You did it!
The face in question should have a one on it. You needed to visualize the numbers you couldn't see and deduce the position of the last die from that.
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A big thanks to http://professorlayton2walkthrough.blogspot.com